Numero 79 Grazie Mille
$4(a^2t^2+c^2x^2+2atcx)+4c^2t^2+4a^2x^2-8atcx$
$4(a^2t^2+c^2x^2+2atcx)+4c^2t^2+4a^2x^2-8atcx$
$4a^2t^2+4c^2x^2+8atcx+4c^2t^2+4a^2x^2-8atcx$
$4a^2t^2+4c^2x^2+4c^2t^2+4a^2x^2$
$4(a^2t^2+c^2x^2+c^2t^2+a^2x^2)$
$4(a^2(t^2+x^2)+c^2(t^2+x^2))$
$4(a^2+c^2)(t^2+x^2)$
4·(a·t + c·x)^2 + (2·c·t - 2·a·x)^2 =
=(4·c^2·x^2 + 8·a·c·t·x + 4·a^2·t^2) +
+(4·a^2·x^2 - 8·a·c·t·x + 4·c^2·t^2)=
=x^2·(4·a^2 + 4·c^2) + (4·a^2·t^2 + 4·c^2·t^2)=
=4·x^2·(a^2 + c^2) + 4·t^2·(a^2 + c^2)=
=(a^2 + c^2)·(4·x^2 + 4·t^2)=
=4·(a^2 + c^2)·(x^2 + t^2)